使用 tikzfading 对两个二维高斯进行卷积-强度问题

Question

我想可视化两个 2D 高斯的卷积（或类似的东西）。为此，我在 tikzfadingfrompicture 环境中声明它们。但是，为了获得所需的结果，而不是在中心太靠近时在中间形成一个整体，我需要将透明度范围设置在 transparent!50 和 transparent!0 之间，这使得输出的图像很难看清。有没有办法增加强度？或者在这种情况下重新调整透明度以使图像更黑？

梅威瑟：

\documentclass[border=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest} 
\usepackage{tikz} 
\usetikzlibrary{fadings} 
\usetikzlibrary{shadings} 
\begin{document} 
\tikzfading[name=fade in, inner color=transparent!100, outer color=transparent!0]
\newcommand\DetFading[4]{ 
  % % 1+2: xy a, 3+4; xy coords b 
  \begin{tikzfadingfrompicture}[name=fadingpict] 
  \begin{scope} 
    \clip (#1,#2) circle(1.5cm); % clip away the non-overlapping parts 
    \clip (#3,#4) circle(1.5cm); 
    \fill [black,path fading=fade in] (#1,#2) circle(1.5cm); 
    \fill [black,path fading=fade in] (#3,#4) circle(1.5cm); 
  \end{scope} 
  \draw [draw=black,line width=2cm] (#1,#2) circle (2.4cm); % remove borders due to clipping 
  \draw [draw=black,line width=2cm] (#3,#4) circle (2.4cm);
\end{tikzfadingfrompicture} 
\node [fill=white,inner sep=0pt,outer sep=0pt,rotate=0,minimum width=3cm,minimum height=3cm] at (#1,#2) (textnode) {}; 
\shade[fill=black,path fading=fadingpict,fit fading=false,fading transform={xshift=#1,yshift=#2},rotate=0] (textnode.south west) rectangle (textnode.north east); } 

\tikzfading[name=fade in half, inner color=transparent!50, outer color=transparent!0] 
\newcommand\DetFadingHalf[4]{ % % 1+2: xy a, 3+4; xy coords b 
\begin{tikzfadingfrompicture}[name=fadingpict] 
    \begin{scope}  
      \clip (#1,#2) circle(1.5cm); % clip away the non-overlapping parts  
      \clip (#3,#4) circle(1.5cm);  
      \fill [black,path fading=fade in half] (#1,#2) circle(1.5cm);  
      \fill [black,path fading=fade in half] (#3,#4) circle(1.5cm);  
    \end{scope}  
    \draw [draw=black,line width=2cm] (#1,#2) circle (2.4cm); % remove borders due to clipping  
    \draw [draw=black,line width=2cm] (#3,#4) circle (2.4cm);  
  \end{tikzfadingfrompicture}  
  \node [fill=white,inner sep=0pt,outer sep=0pt,rotate=0,minimum width=3cm,minimum height=3cm] at (#1,#2) (textnode) {};  
  \shade[fill=black,path fading=fadingpict,fit fading=false,fading transform={xshift=#1,yshift=#2},rotate=0] (textnode.south west) rectangle (textnode.north east); }  
  \begin{tikzpicture}  
    \DetFading{0}{3cm}{1.5cm}{3cm}  
    \DetFading{0}{0cm}{0}{0cm}  
    \DetFadingHalf{3cm}{3cm}{4.5cm}{3cm}  
    \DetFadingHalf{3cm}{0}{3cm}{0} %\node at (3,4) {a};  
  \end{tikzpicture}  
  \end{document}

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结果：